Rationale. Visual features, such as edges and corners, are carried by high-order statistics (also known as multipoint correlations or phase correlations). Analysis of discrimination of "isodipole" textures, which isolate specific kinds of high-order statistics, demonstrates visual sensitivity to these statistics but stops short of analyzing the underlying computations. Here we develop and apply a new psychophysical paradigm that gives insight into these mechanisms. Method. We focus on a canonical isodipole texture, the "even" texture -- in which any 2x2 subarray contains an even number of black and white checks. Stimuli consisted of an array of 14 texture-disks, each containing a sample of a texture drawn from the continuum from random to the pure even texture. Subjects (N=6, 1500 trials) were asked to mouse-click the centroid of the array (presented for 300 ms then masked), weighting the disks according to the evenness of the texture they contained. Performance was modeled by assuming that (1) subjects deploy a "neural filter" to derive a spatial activation map from the stimulus; (2) filter output at stimulus location (x,y) depends on the pattern within the 3x3 subblock of texture centered at (x,y); (3) the subject's estimate of the centroid is the centroid of the filter activation-map produced by the stimulus, plus response noise. Results. Subblocks whose 9 checks were all one polarity produced the highest filter-activation Asolid; subblocks comprising a single 3-check bar and six checks of opposite polarity produced an activation roughly equal to Asolid/2. All other subblocks produced activations less than Asolid/4. A 2-pass procedure showed this model accounted for nearly all of the explainable variance. Conclusions. Visual mechanisms that are sensitive to "even-ness" do not compute four-point correlations per se, but rather are activated selectively by the solid blocks and bars that occur more frequently in the even texture.